Answer:
a)
b) D does not influence the long-term results.
Explanation:
Given that
A = A0 cos(ωt)
This is a linear equation hence the integration factor, I
Now using the characteristics of linear equations
Thus, the initial condition
does not affect the long-term outcome.
Answer:
The water level increases more when the cube is above the raft before it sinks.
Explanation:
The principle involved is based on Archimedes' theory, which states that immersing an object in water will raise the initial water level. This means that the height of the water in the container increases. The increase in water volume corresponds to the volume of the submerged object.
We can consider two scenarios: when the steel cube rests on the raft and when it settles at the pool's bottom.
When the cube rests at the pool’s bottom, the volume will indeed rise, and we can ascertain this using the cube's volume.
Vc = 0.45*0.45*0.45 = 0.0911 [m^3]
When an object floats, it's because the densities of the object and water are in equilibrium.
The formula for density is:
Ro = m/V
where:
m= mass [kg]
V = volume [m^3]
The buoyant force can be calculated with this equation:
Vs > Vc indicates that the combined volume of the raft and the cube exceeds that of the cube alone resting at the bottom of the pool. Hence, when the cube is positioned above the raft, the water level rises more before it becomes submerged.
1) 9.18 s
During the initial phase, the rocket accelerates at
over a time interval of
The final velocity after this period is found using the SUVAT formula:
with initial velocity u = 0. Substituting a1 and t1 gives:
Afterward, the rocket decelerates uniformly at
until it stops, meaning the final velocity is
Again using the SUVAT formula,
and knowing , solve for t2, the time until the rocket halts:
2) 299.9 m
Calculate distances covered in both phases.
Distance in the first phase:
Substituting values from part 1,
Distance in the deceleration phase:
Substituting known values,
Total distance traveled is
d = 82.7 m + 217.2 m = 299.9 m